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Achievable performance bounds for tall MIMO systems

Achievable performance bounds for tall MIMO systems

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In this study, a methodology to compute achievable performance bounds for non-right-invertible, stable, discrete-time MIMO systems is proposed. This methodology is based on the definition of a new performance index, which is the cumulative, squared and exponentially weighted tracking error to a step reference. The results include expressions for the optimal value of this performance index and for the Youla parameter that is able to achieve such performance. For a particular class of single-input multiple-output plants, closed-form expressions depending on the dynamic features of the plant are also obtained. A discussion on the selection of the speed of decay of the exponential weight and its influence on optimal closed-loop stability is included. Numerical examples are presented to illustrate the results.

Inspec keywords: MIMO systems; least mean squares methods; stability; closed loop systems; discrete time systems; performance index; optimal control

Other keywords: single-input multiple-output plants; discrete-time MIMO systems; exponentially weighted tracking error; Youla parameter; optimal closed-loop stability; closed-form expressions; performance index

Subjects: Discrete control systems; Multivariable control systems; Stability in control theory; Optimal control; Interpolation and function approximation (numerical analysis)

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